Answer:
10.3 meters.
Step-by-step explanation:
From Triangle ABC
[tex]\tan 29^\circ =\dfrac{6.3+x}{h} \\h \tan 29^\circ=6.3+x\\h=\dfrac{6.3+x}{\tan 29^\circ}[/tex]
From Triangle ADC
[tex]\tan 19^\circ =\dfrac{x}{h} \\h \tan 19^\circ=x\\h=\dfrac{x}{\tan 19^\circ}[/tex]
Since the values of h are the same
[tex]\dfrac{x}{\tan 19^\circ}=\dfrac{6.3+x}{\tan 29^\circ}\\\\x\tan 29^\circ=\tan 19^\circ(6.3+x)\\x\tan 29^\circ=6.3\tan 19^\circ+x\tan 19^\circ\\x\tan 29^\circ-x\tan 19^\circ=6.3\tan 19^\circ\\x(\tan 29^\circ-\tan 19^\circ)=6.3\tan 19^\circ\\x=\dfrac{6.3\tan 19^\circ}{\tan 29^\circ-\tan 19^\circ} \\x=10.3$ meters (to the nearest tenth of a meter)[/tex]
The height of the first balcony above stage level is 10.3 meters.
